It all depends on the original structure. Houses built in that era have an incredible stability to them. I'm sitting in one right now that is made of solid oak. We just about have to use a jackhammer to hang a set of blinds. The issues I have are mostly to do with pipes. The worst part of the pipes on that house will be left behind. If it is placed on a level lot that doesn't have any settling issues, it should be fine.
In a house of that age, they would probably lose as much of the cypress as they would reclaim. Wood that has been together that long doesn't like to come apart!
Look at those floors, and those window frames! Is that a bead-board ceiling? The bones remind me of my house...